Preliminary discussion
Experiments 5 and 6 use the Emona DATEx to demonstrate the differences you would see on a scope between the output signals of an AM and DSBSC modulator. To refresh your memory, Figure 1 below shows the AM and DSBSC signals that would be produced by identical inputs (for example, a 1kHz sinewave for the message and a 100kHz sinewave for the carrier).
Figure 1
The two signals look different because they contain different sinewaves. That is, they have a different spectral composition. The reason for this is explained by the mathematical models of AM and DSBSC. Side-by-side, it’s easy to see that the equations are a little different.
AM = (DC + message) × the carrier DSBSC = the message × the carrier
And, when the equations are solved for the inputs specified above, we find that the AM and DSBSC signals consist of the following:
AM signal
DSBSC signal
AM DSBSC Description 100kHz - A sinewave at the carrier frequency
101kHz 101kHz A sinewave with a frequency equal to the sum of the carrier and message frequencies (the upper sideband or USB)
99kHz 99kHz A sinewave with a frequency equal to the difference between the carrier and message frequencies (the lower sideband or LSB) As you can see, AM signals include the carrier signal whereas DSBSC signals don’t.
When you think about it, a scope’s display is actually a graph of time (on the X-axis) versus voltage (on the Y-axis). Importantly, graphs plotted this way are said to be drawn in the time domain.
Another way of representing signals like AM and DSBSC signals involves drawing all the sinewaves that they contain on a graph that has frequency for the X-axis instead of time. In other words, they’re drawn in the frequency domain. When the AM and DSBSC signals in Figure 1 are drawn this way, we get the graphs in Figure 2 below.
Figure 2 frequency Voltage or power 100kHz Carrier 101kHz USB 99kHz LSB frequency V or P 100kHz 101kHz USB 99kHz LSB AM DSBSC
Frequency domain representations of complex signals are very useful for thinking about their spectral composition. They give you a tool for visualising the sinewaves that the signal is made up of. They also help you to see how much of the frequency spectrum the signal occupies. This is the signal’s bandwidth and is a critical issue in communications and telecommunications. The bandwidth of AM and DSBSC signals can be calculated in one of two ways. The frequency domain graphs in Figure 2 shows that the signals occupy a portion of the spectrum from the lower sideband up to the upper sideband. That being the case, the bandwidth can be found using the equation:
LSB USB
BW = −
Using this equation we find that the bandwidth of the AM and DSBSC signals in Figure 2 are 2kHz. In situations where the sidebands are made up of more than one sinewave, you must solve the equation using the highest frequency in the USB and the lowest frequency in the LSB. Now, compare the bandwidth of the signals in Figure 2 (2kHz) with the original signals used to produce them (that is, a 1kHz message and a 100kHz carrier). Notice that their bandwidths are twice the frequency of their message. This gives us the second equation for calculating bandwidth:
m
f
BW = 2× where fm = the message frequency
In situations where the message is made up of more than one sinewave, you must solve the equation using the highest frequency in the message.
The experiment
In this experiment you’ll use the Emona DATEx to generate a real AM and DSBSC signal then analyse the spectral elements of the two signals using the NI ELVIS Dynamic Signal Analyzer. It should take you about 50 minutes to complete this experiment.
Equipment
Personal computer with appropriate software installed NI ELVIS plus connecting leads
NI Data Acquisition unit such as the USB-6251 (or a 20MHz dual channel oscilloscope) Emona DATEx experimental add-in module
Procedure
Part A – Setting up the AM modulator
To experiment with AM spectrum analysis, you need an AM signal. The first part of the experiment gets you to set one up.
1. Ensure that the NI ELVIS power switch at the back of the unit is off.
2. Carefully plug the Emona DATEx experimental add-in module into the NI ELVIS. 3. Set the Control Mode switch on the DATEx module (top right corner) to PC Control. 4. Check that the NI Data Acquisition unit is turned off.
5. Connect the NI ELVIS to the NI Data Acquisition unit (DAQ) and connect that to the personal computer (PC).
6. Turn on the NI ELVIS power switch at the back then turn on its Prototyping Board Power switch at the front.
7. Turn on the PC and let it boot-up.
8. Once the boot process is complete, turn on the DAQ then look or listen for the indication that the PC recognises it.
9. Launch the NI ELVIS software.
10. Launch the DATEx soft front-panel (SFP) and check that you have soft control over the DATEx board.
Ask the instructor to check your work before continuing.
11. Slide the NI ELVIS Variable Power Supplies’ negative output Control Mode switch so that it’s no-longer in the Manual position.
12. Launch the Variable Power Supplies VI.
13. Turn the Variable Power Supplies negative output Voltage control to the middle of its travel then minimise the window.
14. Locate the Adder module on the DATEx SFP and turn its soft G and g controls fully anti-clockwise.
15. Connect the set-up shown in Figure 3 below.
Figure 3
16. Launch the NI ELVIS DMM VI (ignore the message about maximum accuracy by clicking OK).
17. Set up the DMM VI for measuring DC voltages.
18. Connect the Adder module’s output to the DMM’s HI input and adjust the module’s soft g control to obtain a 1V DC output.
19. Close the DMM VI.
B A ADDER G GA+gB g MASTER SIGNALS 100kHz SINE 100kHz COS 100kHz DIGITAL 8kHz DIGITAL 2kHz SINE 2kHz DIGITAL SCOPE CH A CH B TRIGGER Y DC AC MULTIPLIER MULTIPLIER kXY X DC Y DC kXY DC X AC VARIABLE DC FUNCTION GENERATOR + ANALOG I/ O ACH1 DAC1 ACH0 DAC0
20. Slide the NI ELVIS Function Generator’s Control Mode switch so that it’s no-longer in the Manual position.
21. Launch the Function Generator’s VI.
22. Press the Function Generator VI’s ON/OFF control to turn it on.
23. Adjust the Function Generator using its soft controls for an output with the following specifications:
Waveshape: Sine
Frequency: 10kHz exactly (as indicated by the frequency counter) Amplitude: About the middle of its travel
DC Offset: 0V
24. You’ll be using the Function Generator VI again later but minimise its window for now. 25. Launch the NI ELVIS Oscilloscope VI.
26. Set up the scope per the procedure in Experiment 1 (page 1-13) with the following changes:
Trigger Source control to Immediate instead of CH A Channel A Coupling control to the DC position instead of AC
Channel A Scale control to the 500mV/div position instead of 1V/div Timebase control to the 50µs/div position instead of 500µs/div 27. Adjust the Adder module’s soft G control to obtain a 1Vp-p sinewave.
28. Set the scope’s Trigger Source control to CH A and set its Trigger Level control to 1V. 29. Activate the scope’s Channel B input to view both the message and the modulated
carrier.
Self check: If the scope’s Scale control for Channel B is set to the 1V/div position, the scope should now display an AM signal with envelopes that are the same shape and size as the message. If not, repeat this process starting from Step 11.
The set-up can be represented by the block diagram in Figure 4 below. It implements the equation: AM = (1VDC + 1Vp-p 10kHz sine) × 4Vp-p 100kHz sine.
Figure 4
Question 1
For the given inputs to the Multiplier module, what are the frequencies of the three sinewaves on its output?
Question 2
Use this information to calculate the AM signal’s bandwidth. Tip: If you’re not sure how to do this, read the preliminary discussion.
Ask the instructor to check your work before continuing. A B Message To Ch.A 100kHz carrier X Y AM signal To Ch.B 10kHz
Part B – Setting up the NI ELVIS Dynamic Signal Analyzer 30. Close the scope’s VI.
31. Launch the NI ELVIS Dynamic Signal Analyzer VI.
Note: If the Dynamic Signal Analyzer VI has launched successfully, your display should look like Figure 5 below.
32. Adjust the Signal Analyzer’s controls as follows: General
Sampling to Run Input Settings
Source Channel to Scope CHB FFT Settings
Frequency Span to 150,000 Resolution to 400
Window to 7 Term B-Harris Triggering
Triggering to FGEN SYNC_OUT Frequency Display Units to dB RMS/Peak to RMS Scale to Auto Voltage Range to ±10V Averaging Mode to RMS Weighting to Exponential # of Averages to 3
Markers to OFF (for now)
Note: If the Signal Analyzer VI has been set up correctly, your display should look like Figure 6 below.
The Signal Analyzer’s display needs a little explaining here. There are actually two displays, a large one on top and a much smaller one underneath. The smaller one is a time domain
representation of the input (in other words, the display is a scope). Notice that it’s showing the AM signal that you set up earlier and saw in Step 29.
The larger of the two displays is the frequency domain representation of the input. Notice that it looks fairly similar to the frequency domain graph for an AM signal in Figure 2 (in the preliminary discussion). The Signal Analyzer’s display doesn’t have single sharp lines for each of the sinewaves present in the signal because the practical implementation of FFT is not as precise as the theoretical expectation.
Part C – Spectrum analysis of an AM signal
The next part of this experiment let’s you analyze the frequency domain representation of the AM signal to see if its frequency components match the values that you mathematically
predicted for Questions 1 and 2.
33. Activate the Signal Analyzer’s markers by pressing the Markers button.
Note 1: When you do, the button should display the word “ON” instead of “OFF”. Note 2: Green horizontal and vertical lines should appear on the Signal Analyzer’s frequency domain display. If you can’t see both lines, turn the Markers button off and back on a couple of times while watching the display.
The NI ELVIS Dynamic Signal Analyzer has two markers M1 and M2 that default to the left most side of the display when the NI ELVIS is first turned on. They’re repositioned by “grabbing” their vertical lines with the mouse and moving the mouse left or right.
34. Use the mouse to grab and slowly move marker M1.
Note: As you do, notice that marker M1 moves along the Signal Analyzer’s trace and that the vertical and horizontal lines move so that they always intersect at M1. 35. Repeat Step 34 for marker M2.
Note: Finer control over the markers’ position is obtained by using the Signal Analyzer’s Marker Position control beneath the Markers ON/OFF button (and just above the HELP button).
The NI ELVIS Dynamic Signal Analyzer includes a tool to measure the difference in magnitude and frequency between the two markers. This information is displayed in green between the upper and lower parts of the display.
36. Move the markers while watching the measurement readout to observe the effect. 37. Position the markers so that they’re on top of each other and note the measurement.
Note: When you do, the measurement of difference in magnitude and frequency should both be zero.
Usefully, when one of the markers is moved to the extreme left of the display, its position on the X-axis is zero. This means that the marker is sitting on 0Hz. It also means that the measurement readout gives an absolute value of frequency for the other marker. This makes sense when you think about it because the readout gives the difference in frequency between the two markers but one of them is zero.
38. Move M1 to the extreme left of the display.
39. Align M2 with the highest point in the AM signal’s lower sideband.
Note: This is the sinewave just to the left of the largest sinewave in the display. 40. Measure the sinewave’s frequency and record this in Table 1 on the next page. 41. Align M2 with the highest point in the AM signal’s carrier and repeat Step 40.
Note: This is the largest sinewave in the display.
42. Align M2 with the highest point in the AM signal’s upper sideband and repeat Step 40. Note: This is the sinewave just to the right of the carrier.
43. Align M1 with the highest point in the AM signal’s lower sideband and measure the AM signal’s bandwidth.
Table 1 LSB frequency Carrier frequency USB frequency Bandwidth Question 3
How do the measured values in Table 1 compare with your theoretically predicted values (see Questions 1 and 2)? Explain any differences.
As an aside, at this point it looks as though the sidebands are nearly as large as the carrier. Moreover, it looks as though there are other substantial sinewaves in the Multiplier module’s output signal. However, this is misleading because the vertical axis is logarithmic (that is, it’s non-linear). The sidebands and these other frequency components are much smaller than the carrier. This can be proven as follows:
44. Set the Signal Analyzer’s Units control to Linear instead of dB.
Note: This sets the vertical axis to a simple linear voltage measurement instead of decibels.
45. Note the relative sizes of the sinewaves in the signal. 46. Return the Signal Analyzer’s Units control to dB.
Ask the instructor to check your work before continuing.
47. Maximise the Function Generator’s VI and increase its output frequency to 20kHz. 48. Use the Signal Analyzer’s two markers to find the AM signal’s new bandwidth. Record
this in Table 2 below.
Note: It’ll take up to thirty seconds for the display to be fully up to date with the change because it’s an average of three sweeps.
49. Increase the Function Generator’s output frequency to 30kHz. 50. Find and record the AM signal’s new bandwidth.
Table 2 Bandwidth for fm = 20kHz Bandwidth for fm = 30kHz Question 4
What’s the relationship between the message signal’s frequency and the AM signal’s bandwidth?
51. Return the Function Generator’s output frequency to 10kHz.
52. Wait until the Signal Analyzer’s frequency domain display has fully updated then disconnect the banana plug to the Multiplier module’s X input.
53. Wait until the display has fully updated then investigate the frequency of the most significant sinewave on the Multiplier module’s output.
Ask the instructor to check your work before continuing.
Question 5
What is this signal?
Question 6
What’s missing and why?
54. Reconnect the banana plug to the Multiplier module’s X input. 55. Disconnect the banana plug to the Multiplier module’s Y input.
56. Wait until the display has fully updated then investigate the frequency of the most significant sinewave on the Multiplier module’s output.
Question 7
What is this signal?
Question 8
Why are the sidebands missing when there’s a message?
Ask the instructor to check your work before continuing.
Part D – Setting up the DSBSC modulator
To experiment with DSBSC spectrum analysis, you need a DSBSC signal. This part of the experiment gets you to set one up.
57. Disassemble the current set-up. 58. Close the Signal Analyzer’s VI.
59. Maximise the Function Generator VI and check that its output frequency is has been returned to 10kHz.
60. Set the Function Generator’s output to 1Vp-p. 61. Connect the set-up shown in Figure 7 below.
Figure 7
This set-up can be represented by the block diagram in Figure 8 on the next page. It implements the equation: DSBSC = 1Vp-p 10kHz sine × 4Vp-p 100kHz sine.
MASTER SIGNALS 100kHz SINE 100kHz COS 100kHz DIGITAL 8kHz DIGITAL 2kHz SINE 2kHz DIGITAL SCOPE CH A CH B TRIGGER Y DC AC MULTIPLIER MULTIPLIER kXY X DC Y DC kXY DC X AC VARIABLE DC FUNCTION GENERATOR + ANALOG I/ O ACH1 DAC1 ACH0 DAC0
Figure 8
62. Launch the NI ELVIS Oscilloscope virtual instrument (VI).
63. Set up the scope per the procedure in Experiment 1 ensuring that the Trigger Source control is set to CH A.
64. Adjust the scope’s Timebase control to view three or so cycles of the Function Generator’s output.
65. Activate the scope’s Channel B input to view the DSBSC signal out of the Multiplier module as well as the message signal.
66. Press the scope’s Autoscale controls for both channels.
Self check: The scope should now display a DSBSC signal with alternating halves of the envelope forming the same shape as the message and is about the same size.
Question 9
For the given inputs to the Multiplier module, what are the frequencies of the two sinewaves on its output?
Question 10
Use this information to calculate the DSBSC signal’s bandwidth. Message To Ch.A Y X DSBSC signal To Ch.B 100kHz carrier 10kHz
Part E – Spectrum analysis of a DSBSC signal 67. Close the scope’s VI.
68. Launch the NI ELVIS Dynamic Signal Analyzer VI and adjust its controls per Step 32. Note: Once done, you should be able to clearly see the DSBSC signal’s two sidebands.
You’ll also see that the signal has a carrier. However, despite appearances, this signal is very small relative to the sidebands (remember, the scale for the Y-axis is decibels which is a logarithmic unit of measurement). Design limitations in implementing DSBSC mean that there will always be a small carrier component in the DSBSC signal. That’s why the second “s” in DSBSC is for “suppressed”.
69. Activate the Signal Analyzer’s markers by pressing the Markers button. 70. Align M1 with the DSBSC signal’s lower sideband.
71. Measure the sinewave’s frequency and record this in Table 3 below. 72. Align M1 with the DSBSC signal’s upper sideband and repeat Step 71.
73. Use the Signal Analyzer’s two markers to determine and record the DSBSC signal’s bandwidth.
Table 3 LSB frequency
USB frequency Bandwidth
Ask the instructor to check your work before continuing.
Question 11
How do the measured values in Table 3 compare with your theoretically predicted values (see Questions 9 and 10)?
Question 12
Compare the DSBSC signal’s bandwidth with the bandwidth for the AM signal with a 10kHz message (in Table 1). What can you say about the bandwidth requirements of AM and DSBSC signals?
74. Find the DSBSC signal’s bandwidth for two other message frequencies (say 20kHz and 30kHz).
Question 13
What’s the relationship between the message signal’s frequency and the DSBSC signal’s bandwidth?
Ask the instructor to check your work before continuing.
Ask the instructor to check your work before finishing.
Name: Class:
Experiment 8 – AM demodulation
Preliminary discussion
If you’ve completed Experiment 5 then you’ve seen what happens when a 2kHz sinewave is used to amplitude modulate a carrier to produce an AM signal. Importantly, you would have seen a key characteristic of an AM signal – its envelopes are the same shape as the message (though the lower envelope is inverted).
Recovering the original message from a modulated carrier is called demodulation and this is the main purpose of communications and telecommunications receivers. The circuit that is widely used to demodulate AM signals is called an envelope detector. The block diagram of an envelope detector is shown in Figure 1 below.
Figure 1
As you can see, the rectifier stage chops the AM signal in half letting only one of its envelopes through (the upper envelope in this case but the lower envelope is just as good). This signal is fed to an RC LPF which tracks the peaks of its input. When the input to the RC LPF is a